#PART 1

Part 1 consists of retrieving CES 4.0 data for the Bay Area. Maps will be produced for the PM2.5 and Asthma rankings. Using the data methodology information in the CalEnviroScreen report, the context of the variables can be determined. Firstly, the asthma variable represents the age-adjusted rate of emergency department visits for asthma per 10,000 people (from 2015 to 2017). Alternatively, the PM2.5 variable is quantified by the annual mean PM2.5 concentration in micrograms per meter cubed (from 2015 to 2017).

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#PART 2

At this stage, the “fitness” of the best-fit line appears to be somewhat correlated with the data. Although, it appears that there is an inflection in the data around 8 on the PM2.5 axis.

#PART 3

## 
## Call:
## lm(formula = Asthma ~ PM2.5, data = ces4_map)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -54.349 -25.752  -9.579  12.833 183.031 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -115.55      13.01  -8.883   <2e-16 ***
## PM2.5          19.77       1.53  12.920   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 37.35 on 1568 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.09621,    Adjusted R-squared:  0.09563 
## F-statistic: 166.9 on 1 and 1568 DF,  p-value: < 2.2e-16

The following can be taken away from the summary of the model:

An increase of 1 unit in PM2.5 is associated with an increase of 19.77 in Asthma; 9.62% of the variation in PM2.5 is explained by the variation in Asthma.

#PART 4

As seen above, the distribution of the data is non-centered. In cases like this when the data is skewed, it can be better fit through a curve. Below is the model with a log transformation applied.

The fitness of the line appears to be a lot more centered on the data with a log transformation applied.

## 
## Call:
## lm(formula = log(Asthma) ~ PM2.5, data = ces4_map)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.00455 -0.46320  0.03286  0.42216  1.75469 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.69911    0.22815   3.064  0.00222 ** 
## PM2.5        0.35557    0.02684  13.247  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.655 on 1568 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.1006, Adjusted R-squared:  0.1001 
## F-statistic: 175.5 on 1 and 1568 DF,  p-value: < 2.2e-16

An increase of 1 unit in PM2.5 is associated with an increase of exp(0.356) or 1.43 times in Asthma; 10.62% of the variation in PM2.5 is explained by the variation in Asthma.

#PART 5

After applying a log-transformation to the y-axis, the distribution of the residuals is no longer skewed and is much more centered.

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's 
## -2.00455 -0.46320  0.03286  0.00000  0.42216  1.75469        1

Based on the above analysis, the area with the most negative residuals is in Stanford, California. This area represents the east portion of the Stanford University campus. An area with the lowest residuals means that data falls the furthest below the line of best fit (when compared to the population of data). This means there is an under-representation of Asthma when compared to the average. This could be because of the long term effects not being seen often as students are constantly moving in and out of the campus.